Line segment bk is the bisector of an isosceles triangle ABC with base BC, angle AKB = 105 *. Find the angles of the triangle.

1) Let the angle ACB = a, then the angle ABC is also equal to a, since the triangle ABC is isosceles (AB = AC). Since ВK divides the angle ABC in half (ВK is the bisector), then the angle KВС = a / 2.
2) Since the angle AKВ = 105 °, and the angles AKВ and ВKС are adjacent, the angle ВKС = 180-105 = 75 °.
3) Consider the ВСК triangle: the sum of its angles = 180 °. Angle C = a, angle B = a / 2, angle K = 75 ° => a + a / 2 + 75 = 180 => a = 70 °.
4) Angle ACB = angle ABC = 70 °. Angle BAC = 180 – 70 – 70 = 40 °.
Answer: 70, 70, 40